US8818781B2 - Method for operating an oil pool based on a reservoir model gradually deformed by means of cosimulations - Google Patents

Method for operating an oil pool based on a reservoir model gradually deformed by means of cosimulations Download PDF

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US8818781B2
US8818781B2 US13/166,030 US201113166030A US8818781B2 US 8818781 B2 US8818781 B2 US 8818781B2 US 201113166030 A US201113166030 A US 201113166030A US 8818781 B2 US8818781 B2 US 8818781B2
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Mickaële Le Ravalec
Sébastien DA VEIGA
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IFP Energies Nouvelles IFPEN
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/66—Subsurface modeling
    • G01V2210/665—Subsurface modeling using geostatistical modeling

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  • the present invention relates to the technical field of the oil industry, and more particularly the operation of subterranean reservoirs, such as oil reservoirs or gas storage sites.
  • Optimizing and operating oil pools rely on a description that is as accurate as possible of the structure, of the petrophysical properties, of the fluid properties, and so on, of the pool being studied. For this, the experts use a tool which makes it possible to reflect these aspects in an approximate manner known as the reservoir model.
  • a model is a model of the subsoil, representative both of its structure and of its behavior.
  • this type of model is represented on a computer, and it is then called a digital model.
  • a reservoir model comprises a meshing or grid, usually three-dimensional, associated with one or more maps of petrophysical properties (porosity, permeability, saturation, etc.). The association process entails assigning values of these petrophysical properties to each of the meshes of the grid.
  • a reservoir model is representative when a reservoir simulation provides estimates of historical data that are very close to the observed data.
  • historical data is used to mean the production data obtained from measurements on the wells in response to the production of the reservoir (production of oil, production of water from one or more wells, gas/oil ratio (GOR), proportion of production water (“water cut”), and/or the repetitive seismic data (4D seismic impedances in one or more regions, etc.).
  • GOR gas/oil ratio
  • water cut proportion of production water
  • a reservoir simulation is a technique that makes it possible to simulate the fluid flows within a reservoir by software called a flow simulator.
  • History matching modifies the parameters of a reservoir model, such as the permeabilities, the porosities or the skins of wells (representing damage around the well), the connections of faults, and so on, to minimize the deviations between the simulated and measured historical data.
  • the parameters may be linked to geographic regions, such as the permeabilities or porosities around a well or several wells.
  • the deviation between real data and simulated data forms a functional, called an objective function.
  • the history matching problem is resolved by minimizing this functional.
  • a representation of the spatial distribution of a petrophysical property is a realization of a random function.
  • a realization is generated from, on the one hand, a mean, a variance and a covariance function which characterizes the spatial variability of the property being studied and, on the other hand, a term or series of random numbers.
  • simulation techniques such as the Gaussian sequential simulation method, the Cholesky method or even the FFT-MA method.
  • Perturbation techniques make it possible to modify a realization of a random function while ensuring the fact that the disturbed realization is also a realization of this same random function.
  • the invention makes it possible to modify a representation of the reservoir, called a reservoir model, to make the representation consistent with the various data collected in the field.
  • the invention relates to an alternative method for operating or controlling an oil pool or reservoir from a reservoir model.
  • This alternative method relies on a history matching in which the reservoir model is gradually deformed by cosimulations which depend on correlation coefficients which then become parameters for adjusting the history matching process.
  • the invention relates to a method for operating an oil pool according to a given operating scheme defined on the basis of a representation of the pool, the representation comprising a meshing associated with at least one map of a property of the pool obtained by a stochastic simulation of a first random function, Simulated Transmissivity Fields.
  • a stochastic simulation of a first random function Simulated Transmissivity Fields.
  • the invention makes it possible to modify a representation of the reservoir, called reservoir model, to make it consistent with the various data collected in the field.
  • the invention relates to an alternative method for operating an oil pool from a reservoir model.
  • This alternative method relies on a history matching in which the reservoir model is gradually deformed by cosimulations which depend on correlation coefficients which then become parameters for adjusting the history matching process.
  • the invention relates to a method for operating an oil pool according to a given operating scheme defined on the basis of a representation of the pool, the representation comprising a meshing associated with at least one map of a property of the pool obtained by a stochastic simulation of a first random function, in which dynamic data are acquired during operation of the pool, and the map being modified to minimize an objective function measuring a difference between the dynamic data and dynamic data simulated by the representation of the pool and a flow simulator.
  • the method comprises the following steps:
  • a correlation coefficient equal to 1 can be chosen in the meshes of the meshing where there is no desire to modify the map, and a correlation coefficient other than 1 is chosen in the meshes of the meshing where there is a desire to modify the map.
  • step iii a set of random numbers which are used to generate the first map is modified, then the method is reiterated at step ii).
  • the representation comprises N maps, N being an integer strictly greater than 1, N ⁇ 1 correlation coefficients between the first random function are chosen and N ⁇ 1 other random functions of the same mean and the same covariance are chosen, and the maps are modified by performing a cosimulation of the first random function and of the N ⁇ 1 other random functions by using the correlation coefficients.
  • FIG. 1 illustrates the method for operating an oil pool according to the invention.
  • FIG. 2 illustrates an application of the cosimulation perturbation method in the case of a perturbation affecting all the meshes of the geological model.
  • FIG. 3 illustrates an application of the cosimulation perturbation method in the case of a perturbation affecting some of the meshes situated at the center of the geological model.
  • FIG. 4 illustrates the history matching step according to the cosimulation perturbation method.
  • FIG. 5 represents the realizations of porosity ( ⁇ ), of horizontal permeability (Kx) and vertical permeability (Kz) generated to populate the five layers (C 1 to C 5 ) of the initial reservoir model.
  • FIG. 6 represents the realizations of porosity (at the top), of horizontal permeability (in the middle) and vertical permeability (at the bottom) generated to populate the five layers of the reservoir model obtained after matching.
  • FIG. 7 illustrates the trend of the objective function (which measures the deviation between the real production data and the corresponding digital responses) as a function of the number of iterations.
  • FIG. 1 illustrates the method for operating an oil pool according to the invention.
  • FIG. 4 illustrates the history matching step. The method mainly comprises four steps:
  • the geological formations are usually highly heterogeneous environments.
  • the modeling of a reservoir that is to say, the construction of a reservoir model representative of the reservoir, entails using construction methods which are called “probabilistic” because of the limited information available (small number of wells, etc.). Because of this, the geological models constructed from these probabilistic methods are called “stochastic models”.
  • the construction of a stochastic reservoir model must first of all depend on the environment of the geological deposit, which makes it possible to represent the major heterogeneities affecting the flow of fluids.
  • the incorporation of the static data in this model involves linear operations and can be done using geostatistical techniques well known to the experts.
  • a reservoir model represented on a computer, includes a grid with N dimensions (N>0 and usually equal to two or three) in which each of the meshes is assigned the value of a property characteristic of the area being studied. This may be, for example, the porosity or the permeability distributed in a reservoir. These values form maps.
  • a model is a grid associated with at least one map.
  • the value of a property characteristic of the area being studied is called regionalized variable.
  • This is a continuous variable, distributed in space, and representative of a physical phenomena. From the mathematical point of view, it is simply a function z(u) that takes a value at each point u (the mesh of the grid) of a field of study D (the grid representative of the reservoir).
  • D the grid representative of the reservoir.
  • the variation of the regionalized variable in this space is too irregular to be able to be formalized by a mathematical equation.
  • the regionalized variable represented by z(u) has both a global aspect, relative to the spatial structure of the phenomenon being studied, and a random local aspect.
  • a random variable is a variable that can take a certain number of realizations z according to a certain probability law.
  • Continuous variables such as the seismic attributes (acoustic impedance) or petrophysical properties (saturation, porosity, permeability) can be modeled by VAs. Because of this, at the point u, the regionalized variable z(u) can be considered to be the realization of a random variable Z.
  • a random function is a set of random variables (VA) defined over a field of study D (the grid representative of the reservoir), that is to say ⁇ Z(u), u*D ⁇ , also denoted Z(u).
  • VA random variables
  • the FA Z(u) makes it possible to take into account both the locally random aspect (at u*, the regionalized variable z(u*) being a VA) and the structured aspect (via the spatial probability law associated with the FA Z(u)).
  • the realizations of a random function provide stochastic reservoir models. From such models, it is possible to assess how to operate the subterranean area being studied. For example, the simulation of the flows in a porous environment represented by digital stochastic models makes it possible, among other things, to predict the production of the reservoir and thus optimize its operation by testing various scenarios.
  • the reservoir model constitutes a representation of the pool. It comprises a meshing associated with at least one map of a characteristic property of the pool. This map is obtained by a stochastic simulation of a first random function. This last step can be described as follows:
  • Dynamic data are therefore acquired during operation of the pool. These are production, well test, drilling time, 4D seismic, and other such data, the particular feature of which is that they vary over time as a function of the fluid flows in the reservoir.
  • This step is performed by means of measuring tools such as flow meters or seismic campaigns.
  • the map (associated with the reservoir model) is modified so as to minimize the objective function measuring the difference between the dynamic data and the dynamic data simulated by the representation of the pool (reservoir model).
  • This step is performed by a computer running technical software called a flow simulator. This software makes it possible to simulate the dynamic data from the representation of the pool.
  • the principles of the cosimulation are explained among other things in the following documents:
  • the method comprises the following steps:
  • the reservoir model is modified by performing a cosimulation of the first random function (Y1) and of the second random function (Y2) by using the correlation coefficient ( ⁇ 12);
  • FIG. 2 shows realizations of porosity y 2 generated from the probability law of Y2knowing Y1 by increasing the correlation coefficient from ⁇ 1 to 1.
  • the initial realization of porosity y 1 corresponds to a correlation coefficient of 1.
  • y 2 is identical to the initial realization y 1 .
  • y 2 is independent of y 1 .
  • y 2 is the reversed image of y 1 .
  • the pool is then operated according to this operating scheme adapted to the reservoir model obtained from the history matching.
  • the cosimulation perturbation method according to the invention can be extended to the case of a local perturbation, by considering the correlation coefficient ⁇ 12 as a function rather than as a scalar: it has the value 1 in the meshes of the model which must not be modified and any other value between ⁇ 1 and 1 in the meshes which must be modified.
  • the cosimulation principle is applied to the random numbers used to generate the realizations of porosity rather than to the realizations of porosity themselves.
  • the procedure can now simulate Z 1 and then Z 2 knowing Z 1 , with Z 1 and Z 2 being two random functions of zero mean and of identity covariance function.
  • z 1 is the set of random numbers used to generate the initial realization of porosity y 1 .
  • the correlation coefficient between z 1 and z 2 is denoted ⁇ 12 .
  • the mean and covariance of Z 2 knowing Z 1 , then become: m 2
  • 1 ⁇ 12 z 1 and C 2
  • 1 (1 ⁇ 12 2 ) I
  • z 2 ⁇ 12 z 1 + ⁇ square root over (1 ⁇ 12 2 ) ⁇ z 1 (2)
  • z 1 (2) is a set of random numbers independent of z 1 .
  • z 2 can then be used as set of random numbers to generate the realization of porosity y 2 . If the correlation coefficient is continuously modified between ⁇ 1 and 1 in the area in which a modification is desired, while keeping this coefficient equal to 1 in the rest of the model, and the same sets of random numbers are kept, a continuous chain of realizations y 2 ( ⁇ 12 ) is obtained, as illustrated in FIG. 3 .
  • the image bottom right represents the value of the correlation coefficient assigned to each mesh: in gray, the coefficient has the value 1, and there is therefore no modification, in black, the coefficient is different from 1 and there is therefore a deformation of the image.
  • the cosimulation perturbation method can also be extended to the case of the cosimulation of N correlated realizations. Then a return to the formulae explained previously is made. They can be used recursively to calculate m 3
  • ⁇ i,i+1 are the correlation coefficients between the realizations of porosity i and i+1. These are all parameters which can be adjusted during the matching process to construct a geological model that confirms the dynamic data.
  • the cosimulation perturbation method has been introduced in relation to realizations of porosity. It applies in the same way to realizations of permeability or of initial saturation, or of any other characteristic property of the reservoir.
  • the field contains oil and gas. It is produced from 6 producing wells located close to the line of contact between the oil and the gas.
  • the production history comprises: 1 year with well tests, 3 years during which the wells are closed, and 4 years of production. During these 8 years, data on pressure (BHFP), on gas/oil ratio (GOR) by volume and on relative quantity of water produced (W CUT) are collected from the wells. The distribution of the porosities and permeabilities in the reservoir is unknown.
  • the goal is then to use the cosimulation perturbation method to construct a geological model reproducing these data, that is to say, a 3D grid with porosity and permeability values assigned to each mesh.
  • a geological model reproducing these data, that is to say, a 3D grid with porosity and permeability values assigned to each mesh.
  • FIG. 4 The organization of the various steps of the method is illustrated by FIG. 4 .
  • a correlation coefficient ( ⁇ 12 ) for the porosity initially with the value 1 is considered.
  • a correlation coefficient ( ⁇ ⁇ Kx ) is determined between the porosity and the horizontal permeability as is another ( ⁇ ⁇ Kz ) between the porosity and the vertical permeability from the available porosity and permeability measurements. For example, reference is made to measurements performed in the laboratory on rock samples taken from the wells.
  • Step 2 Construction of an Initial Reservoir Model
  • the first step is to generate an initial reservoir model (MRi), which takes into account different aspects such as the geological structure, the petrophysical properties, the fluid properties, the wells, and so on.
  • This model is a 3D grid. Since the porosities and permeabilities are unknown, realizations of porosity are generated randomly first of all followed by realizations of horizontal and vertical permeability to populate the meshes. The realizations of permeability and of porosity are correlated: this correlation is reflected in a correlation coefficient.
  • a first realization of porosity is generated first from the first set of random numbers. Then, a realization of porosity is cosimulated (COS) on the basis of the second set of random numbers knowing the initial porosity. The initial realization of porosity ( ⁇ ) is obtained when the correlation coefficient has the value 1. The other two correlation coefficients are then considered. A realization for the horizontal permeability (Kx) and another for the vertical permeability (Kz) are then cosimulated (COS) knowing the porosity. By varying the correlation coefficients, new values are obtained for the porosities and permeabilities. Since the aim is to determine the latter, the correlation coefficients will be treated hereinafter as adjustment parameters.
  • FIG. 5 represents the realizations of porosity ( ⁇ ), of horizontal permeability (Kx) and of vertical permeability (Kz) generated to populate the five layers (C 1 to C 5 ) of the initial reservoir model.
  • Step 4 Flow Simulation (SEc)
  • Simulation is used to reproduce the production scheme of the oil reservoir.
  • the response in production associated with the reservoir model concerned is thus obtained.
  • Step 5 Comparison of the Simulated Responses and of the Production Data (FOb)
  • the digital response from the flow simulator is compared to the actual production data (in the example considered, these are pressures, gas/oil product volume ratios and relative quantity of water produced) measured in the field.
  • the deviation between the data and the results of the simulation is measured by a function, called objective function. If this function is very small (MIN), the reservoir model is considered to be reliable and retained for planning the future management of the field. Otherwise, the porosity and permeability values assigned to the meshes of the model must be modified. In other words, the values of the correlation coefficients must be modified ( ⁇ ) until the objective function is sufficiently small.
  • the reservoir model comprises 5 layers that are mutually independent. For each of them, the porosities and permeabilities are perturbed on the basis of 3 correlation coefficients. The matching of the production data is therefore done by adjusting 15 parameters. At this stage, the 15 correlation coefficients are modified and there is a return to the step 2.
  • the cosimulation process for the porosity depends on 2 sets of random numbers. De facto, by modifying the correlation coefficient attached to the realization of porosity, the process is restricted to a very small portion of the survey space. It is then therefore possible not to have the correct conditions to identify a reservoir model that minimizes the deviation between the actual production data and the corresponding digital responses. To overcome this difficulty, the possibility of exploring other parts of the survey space is exploited: when the step 5 does not provide for any convergence (CONV) toward a minimum value of the objective function, the correlation coefficients determined at this stage are used to update ( ⁇ NbA
  • the reservoir model determined at the end of the matching process is illustrated in FIG. 6 .
  • the responses in production obtained for this model can be used to check that the deviation between the actual data and the simulated data has greatly diminished.
  • the trend of the objective function (FOb) is represented in FIG. 7 as a function of the number of flow simulations (NS) carried out: it changes from 238 to 56.

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US8942966B2 (en) * 2010-10-20 2015-01-27 Conocophillips Company Method for parameterizing and morphing stochastic reservoir models
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